Indirection Mapping for Quasi-Conformal Relief Texturing

Published in I3D '08.

Morgan McGuire, Williams College
Kyle Whitson, Williams College

Paper (17 MB PDF)
Video (24 MB MP4)

Thanks to NVIDIA for donating the GeForce 8800 GPUs used in testing, Sara Carian for proofreading, and Mihai Stoichiu for his complex analysis suggestions.


Heightfield terrain and parallax occlusion mapping (POM) are popular rendering techniques in games. They can be thought of as per-vertex and per-pixel relief methods, which both create texture stretch artifacts at steep slopes.

To ameliorate stretching artifacts, we describe how to precompute an indirection map that transforms traditional texture coordinates into a quasi-conformal parameterization on the relief surface. The map arises from iteratively relaxing a spring network. Because it is independent of the resolution of the base geometry, indirection mapping can be used with POM, heightfields, and any other displacement effect. Noisy textures like grass and stucco can be indirection mapped directly, which is convenient when texturing terrain. For structured textures, we pre-warp the texture by the inverse of the indirection map to maintain appearance.

Our process gives approximately uniform texture resolution on all surfaces. During rendering, the time and space overhead are one texture fetch and one texture map.



Multi-Step Optimizer

Artifacts in Previous Work


  author = {Morgan Mc{G}uire and Kyle Whitson},
  title = {Indirection Mapping for Quasi-Conformal Relief Mapping},
  booktitle = {ACM SIGGRAPH Symposium on Interactive 3D Graphics and Games (I3D '08)},
  year = {2008},
  month = {February},
  url = {},